Coverage, Capacity, and Error Rate Analysis of Multi-Hop Millimeter-Wave Decode and Forward Relaying

Abstract

In this paper, we analyze the end-to-end (e2e) performance of a millimeter-wave (mmWave) multi-hop relay network. The relays in it are decode-and-forward (DF) type. As appropriate for mmWave bands, we incorporate path loss and blockages considering the links to be either line of sight (LOS) or non line of sight (NLOS). The links also experience Nakagami-m fading with different m-parameters for the LOS and NLOS states. We consider two scenarios, namely sparse and dense deployments. In the sparse case, the nodes (relays and the destination) are limited by additive noise only. We derive closed-form expressions for the distribution of equivalent e2e signal-to-noise-ratio (SNR), coverage probability, ergodic capacity, and symbol error rate (SER) for the three classes of digital modulation schemes, namely, binary phase shift keying (BPSK), differential BPSK (DBPSK), and square-quadrature amplitude modulation (QAM). In the dense case, the nodes are limited by interference only. Here, we consider two situations: 1) interference powers are independent and identically distributed (i.i.d.) and 2) they are independent but not identically distributed (i.n.i.d.). For the latter situation, closed-form analysis is exceedingly difficult. Therefore, we use the Welch-Satterthwaite Approximation for the sum of Gamma variables to derive the distribution of the total interference. For both situations, we derive the distribution of signal-to-interference ratio (SIR), coverage probability, ergodic capacity, and SERs for the DBPSK and BPSK. We study how these measures are affected by the number of hops. The accuracy of the analytical results is verified via Monte-Carlo simulation. We show that multi-hop relaying provides significant coverage improvements in blockage-prone mmWave networks.